Elasto‐Plastic Oscillator with Gaussian Excitation

Abstract

A common design criterion for plastic frame or truss structures is that the probability of formation of a mechanism should be below some specified value. However, a mechanism formation need not be catastrophic because the masses of the structure must be accelerated in order to move the mechanism. If the load on the structure varies randomly in time, the load may change such that the plastic movement stops shortly after it has started. The relevant design parameter may therefore be related to the accumulated plastic deformation of the structure rather than to the mere formation of a mechanism. The problem of calculating this plastic movement process is studied for a single degree of freedom linear elastic‐ideal plastic oscillator subject to stationary Gaussian process excitation. It is assumed that the events of plastic movements are rare and of short duration such that the movement process may be modeled as a compound Poisson process. The study concentrates on the calculation of the distribution of the single jumps of the process. The tool for this is the concept of Slepian model process displayed in several interesting applications, in particular by G. Lindgren and co‐workers. Under certain general assumptions it may be concluded that the plastic displacement resulting from a single isolated exceedance of an elasticity limit as a first approximation has an exponential distribution. Special problems appear for narrow band responses with clumping of level crossing. The problem is analysed in some detail at the end of the paper.